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dc.contributor.author
Fichtner, Andreas
dc.contributor.author
Zunino, Andrea
dc.contributor.author
Gebraad, Lars
dc.date.accessioned
2019-02-19T11:18:45Z
dc.date.available
2019-01-29T13:11:00Z
dc.date.available
2019-02-19T11:18:45Z
dc.date.issued
2019-02
dc.identifier.issn
0956-540X
dc.identifier.issn
1365-246X
dc.identifier.other
10.1093/gji/ggy496
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/320896
dc.identifier.doi
10.3929/ethz-b-000320896
dc.description.abstract
We present the theory for and applications of Hamiltonian Monte Carlo (HMC) solutions of linear and nonlinear tomographic problems. HMC rests on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle moving along a trajectory in an extended model space. Using derivatives of the forward equations, HMC is able to make long-distance moves from the current towards a new independent model, thereby promoting model independence, while maintaining high acceptance rates. Following a brief introduction to HMC using common geophysical terminology, we study linear (tomographic) problems. Though these may not be the main target of Monte Carlo methods, they provide valuable insight into the geometry and the tuning of HMC, including the design of suitable mass matrices and the length of Hamiltonian trajectories. This is complemented by a self-contained proof of the HMC algorithm in Appendix A. A series of tomographic/imaging examples is intended to illustrate (i) different variants of HMC, such as constrained and tempered sampling, (ii) the independence of samples produced by the HMC algorithm and (iii) the effects of tuning on the number of samples required to achieve practically useful convergence. Most importantly, we demonstrate the combination of HMC with adjoint techniques. This allows us to solve a fully nonlinear, probabilistic traveltime tomography with several thousand unknowns on a standard laptop computer, without any need for supercomputing resources.
en_US
dc.language.iso
en
en_US
dc.publisher
Oxford University Press
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Inverse theory
en_US
dc.subject
Numerical solutions
en_US
dc.subject
Probability distributions
en_US
dc.subject
Statistical methods
en_US
dc.subject
Seismic tomography
en_US
dc.title
Hamiltonian Monte Carlo solution of tomographic inverse problems
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2018-11-22
ethz.journal.title
Geophysical Journal International
ethz.journal.volume
216
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Geophys. j. int.
ethz.pages.start
1344
en_US
ethz.pages.end
1363
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.publication.place
Oxford
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02330 - Dep. Erdwissenschaften / Dep. of Earth Sciences::02506 - Institut für Geophysik / Institute of Geophysics::03971 - Fichtner, Andreas / Fichtner, Andreas
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02330 - Dep. Erdwissenschaften / Dep. of Earth Sciences::02506 - Institut für Geophysik / Institute of Geophysics::03971 - Fichtner, Andreas / Fichtner, Andreas
en_US
ethz.date.deposited
2019-01-29T13:11:02Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2019-02-19T11:18:55Z
ethz.rosetta.lastUpdated
2019-02-19T11:18:55Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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